Oblique Bayesian additive regression trees

• URL: http://arxiv.org/abs/2411.08849v1
• Date: Wed, 13 Nov 2024 18:29:58 GMT
• Title: Oblique Bayesian additive regression trees
• Authors: Paul-Hieu V. Nguyen, Ryan Yee, Sameer K. Deshpande,
• Abstract summary: Current implementations of Bayesian Additive Regression Trees (BART) are based on axis-aligned decision rules. We develop an oblique version of BART that leverages a data-adaptive decision rule. We systematically compare our oblique BART to axis-aligned BART and other tree ensemble methods, finding that oblique BART was competitive with -- and sometimes much better than -- those methods.
• Score: 0.5356944479760104
• License:
• Abstract: Current implementations of Bayesian Additive Regression Trees (BART) are based on axis-aligned decision rules that recursively partition the feature space using a single feature at a time. Several authors have demonstrated that oblique trees, whose decision rules are based on linear combinations of features, can sometimes yield better predictions than axis-aligned trees and exhibit excellent theoretical properties. We develop an oblique version of BART that leverages a data-adaptive decision rule prior that recursively partitions the feature space along random hyperplanes. Using several synthetic and real-world benchmark datasets, we systematically compared our oblique BART implementation to axis-aligned BART and other tree ensemble methods, finding that oblique BART was competitive with -- and sometimes much better than -- those methods.

Related papers

• Learning a Decision Tree Algorithm with Transformers [75.96920867382859]
  We introduce MetaTree, a transformer-based model trained via meta-learning to directly produce strong decision trees. We fit both greedy decision trees and globally optimized decision trees on a large number of datasets, and train MetaTree to produce only the trees that achieve strong generalization performance.
  arXiv  Detail & Related papers  (2024-02-06T07:40:53Z)
• flexBART: Flexible Bayesian regression trees with categorical predictors [0.6577148087211809]
  Most implementations of Bayesian additive regression trees (BART) one-hot encode categorical predictors, replacing each one with several binary indicators. We re-implement BART with regression trees that can assign multiple levels to both branches of a decision tree node. Our re-implementation, which is available in the flexBART package, often yields improved out-of-sample predictive performance and scales better to larger datasets.
  arXiv  Detail & Related papers  (2022-11-08T18:52:37Z)
• Contextual Decision Trees [62.997667081978825]
  We propose a multi-armed contextual bandit recommendation framework for feature-based selection of a single shallow tree of the learned ensemble. The trained system, which works on top of the Random Forest, dynamically identifies a base predictor that is responsible for providing the final output.
  arXiv  Detail & Related papers  (2022-07-13T17:05:08Z)
• Hierarchical Embedded Bayesian Additive Regression Trees [0.0]
  HE-BART allows for random effects to be included at the terminal node level of a set of regression trees. Using simulated and real-world examples, we demonstrate that HE-BART yields superior predictions for many of the standard mixed effects models' example data sets. In a future version of this paper, we outline its use in larger, more advanced data sets and structures.
  arXiv  Detail & Related papers  (2022-04-14T19:56:03Z)
• GP-BART: a novel Bayesian additive regression trees approach using Gaussian processes [1.03590082373586]
  The GP-BART model is an extension of BART which addresses the limitation by assuming GP priors for the predictions of each terminal node among all trees. The model's effectiveness is demonstrated through applications to simulated and real-world data, surpassing the performance of traditional modeling approaches in various scenarios.
  arXiv  Detail & Related papers  (2022-04-05T11:18:44Z)
• Unfolding Projection-free SDP Relaxation of Binary Graph Classifier via GDPA Linearization [59.87663954467815]
  Algorithm unfolding creates an interpretable and parsimonious neural network architecture by implementing each iteration of a model-based algorithm as a neural layer. In this paper, leveraging a recent linear algebraic theorem called Gershgorin disc perfect alignment (GDPA), we unroll a projection-free algorithm for semi-definite programming relaxation (SDR) of a binary graph. Experimental results show that our unrolled network outperformed pure model-based graph classifiers, and achieved comparable performance to pure data-driven networks but using far fewer parameters.
  arXiv  Detail & Related papers  (2021-09-10T07:01:15Z)
• Accounting for shared covariates in semi-parametric Bayesian additive regression trees [0.0]
  We propose some extensions to semi-parametric models based on Bayesian additive regression trees (BART) The main novelty in our approach lies in the way we change the tree-generation moves in BART to deal with this bias. We show competitive performance when compared to regression models, alternative formulations of semi-parametric BART, and other tree-based methods.
  arXiv  Detail & Related papers  (2021-08-17T13:58:44Z)
• Improved Branch and Bound for Neural Network Verification via Lagrangian Decomposition [161.09660864941603]
  We improve the scalability of Branch and Bound (BaB) algorithms for formally proving input-output properties of neural networks. We present a novel activation-based branching strategy and a BaB framework, named Branch and Dual Network Bound (BaDNB) BaDNB outperforms previous complete verification systems by a large margin, cutting average verification times by factors up to 50 on adversarial properties.
  arXiv  Detail & Related papers  (2021-04-14T09:22:42Z)
• Rethinking Learnable Tree Filter for Generic Feature Transform [71.77463476808585]
  Learnable Tree Filter presents a remarkable approach to model structure-preserving relations for semantic segmentation. To relax the geometric constraint, we give the analysis by reformulating it as a Markov Random Field and introduce a learnable unary term. For semantic segmentation, we achieve leading performance (82.1% mIoU) on the Cityscapes benchmark without bells-and-whistles.
  arXiv  Detail & Related papers  (2020-12-07T07:16:47Z)
• Convex Polytope Trees [57.56078843831244]
  convex polytope trees (CPT) are proposed to expand the family of decision trees by an interpretable generalization of their decision boundary. We develop a greedy method to efficiently construct CPT and scalable end-to-end training algorithms for the tree parameters when the tree structure is given.
  arXiv  Detail & Related papers  (2020-10-21T19:38:57Z)
• Bayesian Additive Regression Trees with Model Trees [0.0]
  We introduce an extension of BART, called Model Trees BART (MOTR-BART) MOTR-BART considers piecewise linear functions at node levels instead of piecewise constants. In our approach, local linearities are captured more efficiently and fewer trees are required to achieve equal or better performance than BART.
  arXiv  Detail & Related papers  (2020-06-12T22:19:58Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.